Solve {l}{3x+5/4=5x+10/2}{y=75}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{3 x + 5}{4} = \frac{5 x + 10}{2} }\\ { y = 75 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=75$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$3x+5=2\left(5x+10\right)$$

Use the distributive property to multiply 2 by 5x+10.

$$3x+5=10x+20$$

Subtract 10x from both sides.

$$3x+5-10x=20$$

Combine 3x and -10x to get -7x.

$$-7x+5=20$$

Subtract 5 from both sides.

$$-7x=20-5$$

Subtract 5 from 20 to get 15.

$$-7x=15$$

Divide both sides by -7.

$$x=-\frac{15}{7}$$

The system is now solved.

$$x=-\frac{15}{7} y=75 z=75$$